Geodesic
Coding knots by $T$-graphs
Contemporary Mathematics. Fundamental Directions, Algebra, Geometry, and Topology, Tome 66 (2020) no. 4, pp. 531-543.

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In this paper, knots are considered as smooth embeddings of a circle into $\mathbb R^3$ defined by their flat diagrams. We propose a new method of coding knots by $T$-graphs describing the torsion structure on a flat diagram. For this method of coding, we introduce conceptions of a cycle and a block and describe transformations of $T$-graphs under the first and the third Reidemeister moves applied to the flat diagram of a knot. 
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O. N. Biryukov. Coding knots by $T$-graphs. Contemporary Mathematics. Fundamental Directions, Algebra, Geometry, and Topology, Tome 66 (2020) no. 4, pp. 531-543. http://geodesic.mathdoc.fr/item/CMFD_2020_66_4_a0/

[1] O. N. Biryukov, “Ridgeless knots”, Bull. State Soc.-Hum. Univ., 2019, no. 3 (35), 18–23 (in Russian)

[2] S. V. Duzhin, S. V. Chmutov, “Knots and their invariants”, Mathematical Enlightenment, 3, MTsNMO, M., 1999, 59–93 (in Russian)

[3] I. A. Dynnikov, “Recognition algorithms in knot theory”, Progr. Math. Sci., 58:6 (2003), 45–92 (in Russian) | MR | Zbl

[4] R. Crowell, R. Fox, Introduction to Knot Theory, Mir, M., 1967 (in Russian) | MR

[5] V. O. Manturov, Knot Theory, NITs Reg. Khaot. Dinam., M.–Izhevsk, 2005 (in Russian)

[6] A. B. Sosinskiy, Nodes. Timeline of One Mathematical Theory, MTsNMO, M., 2005 (in Russian)

[7] Hass J., “Algorithms for recognizing knots and 3-manifolds”, Chaos Solitons Fractals, 9:4-5 (1998), 569–581 | DOI | MR | Zbl